Take modulo and since is prime to it , there is an inverse of it , let

, it is deduced by using the fact that is an integer .

Consider

It should be divisible by if is prime to but we have each term is prime , we have the product contains prime factors that all are greater than , which is prime to . Therefore , is prime to is false for and we have that contains all prime .

Consider , ,

contains these two prime numbers but not also . It is not true that every prime , must divide a , it should be